Say I am rolling a 20-sided die. What is the expected number of rolls to have rolled each number?

I haven't taken statistics in a while so my syntax might be off but this question has been bugging me for a while. Any help or direction is much appreciated.

  • $\begingroup$ is this a homework question? please add self study tag $\endgroup$ – Haitao Du Jul 15 '16 at 14:06
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    $\begingroup$ Hey, this isn't a homework question, it's related to a forum event that I am helping run that involves rolling all possible numbers on a 20 sided-die. Just wanted to make sure that the event is running for an appropriate amount of time that makes "winning" not impossible/highly improbable. I've added the tag though $\endgroup$ – user123424 Jul 15 '16 at 14:11
  • $\begingroup$ See posts on the coupon collector problem. $\endgroup$ – whuber Jul 15 '16 at 14:38
  • $\begingroup$ I removed the self-study tag because it was put there only under peer pressure and does not seem appropriate. :-) $\endgroup$ – whuber Jul 15 '16 at 14:40
  • $\begingroup$ Given the objective of the exercise, as provided in your comment, you shouldn't be satisfied with knowing just the expected number of rolls. Anyhow, see en.wikipedia.org/wiki/Coupon_collector%27s_problem . Can you show us a picture of the 20-sided die?. $\endgroup$ – Mark L. Stone Jul 15 '16 at 14:42